化简 (3sqrt(p)-2sqrt(q))^2

解答

化简

(3 p - 2 q)^{2}

9 p - 12 p q + 4 q

求解步骤

(3 p - 2 q)^{2}

使用完全平方公式:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(3 p - 2 q)^{2} = (3 p)^{2} - 2 \cdot 3 p \cdot 2 q + (2 q)^{2}

= (3 p)^{2} - 2 \cdot 3 p \cdot 2 q + (2 q)^{2}

(3 p)^{2} = 9 p

- 2 \cdot 3 p \cdot 2 q = - 12 p q

(2 q)^{2} = 4 q

= 9 p - 12 p q + 4 q

e x p an d (a (1 - cos (t))^{2} + (a sin (t)) 2)

e x p an d 7 (12 + 2)

e x p an d (3^{\frac{3}{4}} + 3)^{2}

e x p an d \frac{( x + 1 ) ( x - 1 )}{x ^{2}}

e x p an d r^{\frac{2}{5}} (r^{\frac{3}{5}} + r^{\frac{8}{5}})